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CLASSIC KOSMOS AND CONTEMPORARY SCIENCE



 
 
 
 

dialectical constructions in Classic philosophy

 

0. Dialectics is a soul of Classical philosophy, and the constructions of this philosophy have remained and will remain in any dialectics. Dialectics is the most exact knowledge, it is the very life given in concepts and therefore rather distant from the life itself which is not conceptual or exact. But according its object dialectics is the life, and there are no constructs closer to life. Therefore Greek dialectics has originated in the depths of myth (Pythagoreism), evolved as the perception of myth (PLATON and PLOTINUS), and concluded as the construction of ultimate dialectical mythology (PROCLUS).

1. In Pythagoreism we clearly see the mythology as a womb of dialectics: Pythagoric Hieros logos namely because of its mythological operationalism requires for its categorialization through diaeresis into number (Noys) and into what later will become an apeiron.read note. Then dialectical thought proceeds further, and creates systems and hierarchies; monad (ether) is higher than dyas (chaos, apeiron), it is the principle of identity, whereas the latter is the principle of changeread note. But here we still not find the differentiation between eidos and fact, and in the concept of that primaeval matter (hyle) are in still undiscerned unity both Platonic (aoristos kath' ayten) and naturalistic Aristotelian outlook reflecting the yet incomplete nucleation of dialectics from within the naturalism. -Third principle, Chronos, somewhat resembles Plotinian soul. Finally, fourth principle, Abyss (Procl. comm. Tim. 1, 385, 27 - 386, 3), Adrasteia, Anagke, Dike, Nomos, and here is felt the latter To Hen, which embraces the entire tetractid, which is the apophatic Darkness for the mortals, and from the depths of this hypernoetic Zeus comes the divine One until it reaches the sacred Tetraktys. All these Plotinian concepts are there in nuce. The mighty Chronos gave rise in the Ether the splendid Egg, i.e., the primaeval hyle concentrated in its core begets the ovum mundi, fertilized by the Ether (Noys), and out of this Egg hatch the various Numbers, generating forms and senses (Big Bang?) filling the whole world. From these Orphic-Pythagoric cosmologies the one moment is very clear: the anticipation of Platonic antithesis of idea and matter, the antithesis of Phanes and Night, which both produce Light. When the primaeval tetractid begets the son of Ether, second Noys, that first mundane deity acting in the newly created world, Phanes, Pan, Metis,- and Eros. This immense creativity of real world spits fire, which splits the spherical matter into heaven and earth, and the dark abyss between them - Phanes begot the Night; and more: the setting of primaeval Fire remained in the form of Light, and Heat. Noys cannot create without matter, and it cannot differentiate itself into the creatures: it needs meon, Phanes searches high and low for its beloved bride, for Night, and only then it becomes creative, and any real thing is the ensemble of idea and matter. In any subsequent tetractids or decades this principle will repeat and repeat itself, and here methodological inference: dialectical consciousness feels the difference between the dialectics itself and its applications.
 

2. This static dialectics postulating the fundamental unity between the number and thing, because any thing has numerical identity, requires the pleroma of mystical insight especially in this still mythological phase, require the ability to see with e.g., ION OF CHYOS, the unity of synesis (Noys), kratos and tyche in any thing, but, of course, the exact categorical contents of these terms are very problematic. Very good text: Diels 45B17 and 45A8.
 

3. But the necessity for the refinement of the concept of idea created also the dynamic dialectics which is clearly the same as the latter dialectics of PLATON and PLOTINUS. Theories of POLYKLETOS (when the initial typoi are formed and differentiated the different eidoi are created (28B1): here Platonic usage of typos, morphe and eidos), EURYTAS with his arithmois eidetikois resembling the concepts of CANTOR with their expressed intellectual and intuitive clarity. On these theories the concept of idea (intelligible visage of thing) has been crafted (45B4), and the only means to understand all these numerical interpretations of abstract or real entities is the identification of Pythagoric arithmos and number of CANTOR: arithmos is Gestaltqualitaet of thing. In such a way any concept of Idea finally became the concept of unity, of to hen, accelerated by the mythological necessity to do this. The anticipation of Plotinian science about three substances in latter Pythagoreism: unity is :

1) absolute, hyper-oysiodes principle of all being;

2) unity as the element of anything, principle of form and limit as opposed to amorphity and apeiron;

3) concrete All-Einheit, unity in manyness.

Of course, the To hen of PLOTINUS is even more than unity, Noys and soul are unities, but only as the united manynesses (Noys), and united times in the realm of Noys which devotes itself for the disintegration into individualities (Soul). Also, the third entity, after One and Number, emerged, the living Kosmos, beloved object of Pythagoric digressions.
 

4. Also Pythagoreism was very conscious of the ideality of dialectical constructions as their uniting factor (45B8).

5. EKPHANTES: thing is composed of megethos, schema, and dynamis, and moved by noys. Kosmos is idea of this noys, and therefore it is beautifully spherical (38, 1). Therefore:

1) any movement is unexplainable naturalistically;

2) kosmos is governed by dynamis, the action of Noys and Soul;

3) as the result of this action (energeia?) the Kosmos is created and maintained as the reflection (mimesis?) of Noys;

4) kosmos is made of atoms (eidoi?) and nothingness (meon?);

5) any thing has its ideal contents (dynamis) originating from the corresponding eidos, number, schema, and perceived as some quality and quantity (megethos).

Maybe this is not very historical, but we should be conscious the dynamis is the better part of entire dialectics of PLATON!

Sujet of Phanes and Nyx, and many others, is the immediate precursor of science about peras and apeiron, science of opposite and difference. The Pythagoric opposition of one and aoriston dyas is the vehicle of entire "Timaeus". PYTHAGORAS (45B15): "One of his principles represents the poietikon aition kai eidikon which is deity - Noys, whereas another - the pathetikon te kai hylikon, which is the visible kosmos". This antithesis is the grounds for entire dialectics, and, therefore, for entire idealism. The fundamental principle of thought is that ab initio any intellect should generate the difference in itself, because prior to that any reasoning is impossible. Any difference is commensurate to the intensity of reasoning, the degree of differentiation represents the degree of mentality. Here is the origins of dialectics, i.e., self-dependent affirmation of intellect, and here are entire PLATON, PLOTINUS, FICHTE, HEGEL, etc. Antithesis of one and other, eidos and meon, light and darkness is the obligate starting point of any dialectical thinking. The first word of dialectics are: if something is at all this means that it is simultaneously some other. Without it - the undifferentiated darkness of anything and nothing, where any reason is helpless. This is the most precious gift of old Pythagoreism for all the dialectics read note.
 

6. The most striking feature of these old systems, esp. that of PHILOLAUS, is the clear understanding of arithmetic ideality. Decade is the eidos of kosmos (32A13), it is most sacred, most natural technikon eidos for all of the world, aph' heaytes and not bethought by us or accidental. Pythagoreans see the kosmos in its eidos, and this eidos contains everything (35B5). It is not separate of kosmos: there is no hen epekeina tes oysias (32A10): any unity is the unity of many,- here clearly the differentiation between sense and fact. But this ideality also requires the common unity of idea and kosmos, and here it is (32B7, 8, A21), albeit not very clear, but the antithesis of peras and apeiron is, along with their synthesis in the concept of number (DIELS, Phil.B3 - an analogue of 20 chapter of Parmenides). And more, in fr. 11: it is the number what grants us the ability to know, the origins of all sciences. read note

7. The first dialectical system is the system of PLATON. He defines it as the art, or science, to discern the life of idea itself, and this idea is some concrete unity of separates and separation of any unity, therefore its method is the insight into sets as ideal unities, given in their coordinated differentiation. And this science is very hard. The concrete contents of these terms is being as unity of peras and apeiron read notebegetting number. Ideas and eidoi of R.P. in Phileb. 17 are numbers, and dialectical method is applied to them to differentiate one from other and defined from indefinite.read note . From there no more progress is made neither by PLOTINUS, nor FICHTE and HEGEL .This is the genuine dialectics in its purest form uncompromised by naturalistic logic of ARISTOTELESread note. Any dialectics is based on the intuitions of light, fixes limits, and if there are no perceptible difference between light and darkness. All eidology and all ideas collapse along with any mentality. But world is light, descending from the absolute To hen and sinking into absolute darkness, absolute nothing, or meon. The task for intellect is to contemplate these visages of light. These visages are the sense of things, and these senses are senses of concepts, and operation by these concepts means to operate the visages of things. These are eidoi of things, ideas of them, the radiation of them, because the light alone is seen, is be-sensed. And when we see this visage made from many of limits with meonal darkness, we see this as unity, as one, as number, and within this number we could discern more differences, and this arithmos turns into apeiron for new arithmos, etc., etc. This is the dialectics of ideas, with which we will be acquainted throughout this entire book, and it is the heritage of Pythagoreism, born into the womb of myth, lived as a beautiful youth in the system of PLATON emanating the great faith in life and love, reaped the fruits of wisdom and sank into it again in the great synthesis of PLOTIN and PROCLUS.

Our task thus is to reconstruct the entire system of Classical dialectics in its pure form devoid of any accidentality and having all sequiturs drawn until their logical completeness.

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notes for this chapter


 

n15

Main authority of older stages of Greek religion is VYACHESLAV IVANOV in his treatise "Dionysus and prae-Dionysiasm", Baku, 1923. He wrote (p. 277) that the striking characteristics of orgiasm as principal direction of religious thought are these three:

1) identity between orgiastic offering and orgiastic deity or its equivalent;

2) identity between orgiastics and their deity;

3) double understanding of that deity:

a) as master of both earthly and underground realms;
b) simultaneously as offering for himself and as the hierophant which did that offering.

 

 
 
 
 
 

This is because it is thought as principle of life and death, and in active as passive meaning as killing and killed.

Op. cit., pp. 156-157: Apollo is the principle of unity, its essence is monad, whereas Dionysus is the principle of manyness. He is the deity of disintegration, and, nonetheless, the unity impersonated by him, belittling itself, victimizes his divine pleroma and wholeness and therefore, by ex-stasis, creates the manyness of new wholes, and this is the principle of dyas. This principle coordinates with the monadiness of Apollo and identifies with it in the proprietary monadiness of Dionysus, because the dyas is impossible without monas which is resident also in Dionysos. Apollonic monas in the world of Dionysos is immanent for him, as esse is immanent to fieri, and the principle of conservation of personal identity in the other realm if himself, in the realm of death, without what the palingenesis would be impossible. And Apollon gives for him the strength of identity in the streams of disparation (Procl. in Alcib. 391 Cous.). Also in Crat 109, 9-21: meriste demioyrgia is dependent upon the dionysical monad, separating minds from the common noys, and souls from the common Soul, sensual eide from ton oikeion holoteton. Of course, here the immediate incorporation of ancient mystic and mythic concepts. Also Damasc. pr. pr. 40, 123.

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n18

Cf. Procl. in Tim. 1, 17, 13-15, 20-30; 36, 15-20; 78, 6-11; and 87, 25-26: brief and clear formulation: dia gar diados he mona proeisin epi ten telesioyrgon ton holon pronoian; 153, 30; 175, 21-2: apeiria kai skotos onomazomene kai alogia kai maetria kai heteroioseos arche kai dyas, ktl. Also Damasc. pr. pr. 117, 118 - cf. 163. These are loc. comm.

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n24

The intuition that eidos is some Gestalt, visage, agalma, made visible by casting the light on it and by the emiting the light itself, is very fundamental. PLOTINUS loves to speak about light, and in this respect there are few thinkers with the same intensity of photonic way of thinking (DION. AREOPAGITES, SIMEON NEW TH., and PALAMAS), and the affinity of all these systems is absolutely irrefutable. Good reviews: H. F. MUELLER, Dionysios, Proclos, Plotinos: Beitr. z. Gas. d. Philos. Mittelalt. 20: h. 3-4, and O. WALZEL, Plotins Begriff d. aesth. Form: N. Jahrb. f. d. klass. Altert.: 73, 3, 190.

Any noetic object, even number, is for PLOTIN"some noetic agalma, standing as just emerged out of depths of itself" (6, 6, 6). It is very characteristic phrase for such a mathematical and sober mystic as PLOTIN. He sees sharp noetic graffiti. Numbers for him are such sharp, clearly formed, as artistically molded statuarities. These are eidoi, and LOSEV principally refuses to translate this Greek technical term.

PLATON himself (Phaedr. 259b sqq) also tends to describe his eidetic insights this way.

For nice reading see Plot. 1, 6, 9.

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my note about number

the fundamental value of the number is somewhat difficult to grasp. To clarify things a bit I provide here a small excerpt of my old correspondence in listserver about these numbers. It as I think fits here nicely. It is from discussion about Arist. Metaph., first book.
 

Of course, these places are incomprehensible, if one does not tries to re-constitute the Platonic doctrine of arithmology. Losev even finds in the Platonic agrapha (mainly conveyed by our book) the separate, fifth stage of development of Platonic theory of ideas, and call it arithmologic. It occurs that the easiest way to comprehend this ninth chapter is to set up all investigation upside down. Lets open the Inst. theol. of Proclus: 20-21: "in One which is primaeval to all, is a manyness of unities, <...> so after the primaeval one are unities, etc."; 117: any number is a metron of oysia; 116: it is possible to be partook in numbers, but not in One; 118-120: pronoia and hyper of numbers; 123: numbers are cognoscible; 125, 131, 144: numbers make all via their energies; 126, 132: hierarchy of numbers; 140: numbers take their potencies from the energy of One and, in their turn, disperse them through all the inferior spheres of being.

> Part ii, 991b27-993a10

>

> j. another class of no.s must be postulated, for arithmetic, b27

Of course, these Proclian Numbers are not values, or plain mathematical quantities. Meonically speaking, the energy of Number is exactly the cause why when got up in the morning you do not find another you munching with appetite your breakfast, or why you have no problems with, say, a dozen of boots. Numbers are principles of actualization of any numerically one, and forces which define and maintain this actualization. Any one before receiving an oysia, at first must be one.

Numbers of math are absolutely homogeneous, countable, add-able, etc, whereas these ideal numbers each have their own visage, character, and a field of their energetical action. In Theol. arithm. of Iamblichus all of them are as living things each with their own personality. The notion of this is found in any mythology and language, and it is used in magical practice.

To make things clear lets have a look in (neo)platonic table of categories, upper part:

1. The One (above any definition and therefore not a category, but a principle of any categorialization): 1.1. One as absolutely unthinkable. 1.2. One as relatively unthinkable (as a prime moment of any dialectical construction, absolute unity, 1st hypothesis of Parmenides). ! 1.3. One as coordinated with meon (potency of any oysia, or ! Number. 1.4. Number as eidos. 1.5. Eidetic number. These latter two are only in the late Neoplatonism. 2. Oysia, or Noys, etc.

So, Number is before Noys and is more energetically being than it. It is metaxy the One and Oysia.

Aristoteles later, in 13 book, wonders how these Numbers could be not add-able and incommensurable, and cannot comprehend that they are absolutely different categories from math numbers and even are not the principles of them. But from here, b27-31 it is clear that Platon ascribed them specific quality and not held them as quantitative constructions, and operations with them are not arithmetical but of logical and dialectical nature.

About hypo tinon: it seems not substantial whether Plato hypostasized the sphere of middleness or not in 987b16. It is sufficiently clear that he really has a kind of above table of categories in mind. The signs of degradation of Academy after Platon's death are overwhelming in Metaphysics. The ideal qualitative-ness of number is an obligate sequitur of Parmenides and Philebus. As we have seen in ch. 6, 987b14 ff., this metaxy is parallel applicable to the math numbers as metaxy between the eidos and thing a bit lower in the table of categories.

> l. how is there a collective one? a1-a2

In his account Aristoteles stresses the absolute individuality of these hyper-noetic numbers. That the two follows one and four follows three is only their accidens, but their substantial qualitativeness is unique and mutually incomparable. This means that ideal Numbers are not smaller and not bigger, they are all equal. It is clear only from that in this stage of categorialization we yet have not derived the category of quantity, it will appear only in the realm of Oysia. Book 13, ch. 6: they differ only in eidos due their eiconical nature, because this nature too is eidetical.

The problem of unity of these Numbers, if not addressed by Platon himself, has been solved in later Neoplatonism, see, e.g. Proclian doctrine about ex henadon (inst. theol. 5, 6) and its explicit application to Numbers in 113.

> n. difficulty deriving dimensions from oneanother, points or

> number. They are different genera. Plato resisted all this as

> the business of geometricians, a10-a24

This wonderful place about indivisible lines: line cannot be defined as the set of points because any such definition involves some apriori principle of linearity. Here Platon and Xenocrates give the new concept, concept of continuum, and also the means by which the creative energeia of these Numbers makes the kosmos. Continuum is composed of elements which presupposes their participation in that continuum: so any point of line has the idea of direction of a whole manifold. This old (neo)platonic concept was acknowledged in full scale only when the so called "naive" theory of sets stalked the manifolds which do not appeared continual: first of them was the set of Cantor (Cantors dust, the simplest fractal, a mathematical object existing in a space having not a rational number of dimensions). This is in connection with the eiconical character of numbers: the theory of fractals involves the fundamental constants (e.g., dimensionality of Cantor's set: ln2/ln3, constants of metrical universality: 4.669, 1.4011552, Lyapunov's indices) in addition to the fundamental numbers characterizing the kosmos, such as gravitational and cosmological constants, etc. Some vague connection with anthropic principle is also discernible. Our kosmos is more complicated than usually thought.

Another idea, about the mechanism by which numbers govern the kosmos, is traced in connection with the process of demiurgy described in Timaeus. These ideal numbers energetically act, and their action is so complex and amazing that Platon there composed a mythological structure involving the theory of stoicheia, the construction of triangles which are the subatomic structures in making the forms of more dimensions, and overall trend to subject the action of these hypernoetic energies to the smallest constituents of kosmos, which are similar to these numbers. Needless to say, the contemporary theories of phase transitions, of catastrophes and dynamic instabilities are going the same pathway and yielding the same results: that the structural, eikonic nature of mathematic (eidetic) theories is not only governing the process of meonical being, but also even visible in the computer screen. Platonic stoicheia seem to be the planes, not even lines.

Here I am not trying to modernize Platonic arithmological doctrine. Simply it involves the same mythology as the newest provinces of theory of matter, I refer to the works of Prigogine, Thom, Haken, Berge, Pomeau, etc. Also cf. Procl. in R.P. II, 27, 6-7.

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my note about peras

Pythagoreans loved to ramble about these matters very much. CARL HUFFMAN even says that those places are a bit perplexing (Phil. Crot., p. 102, about Fr. 2, but he deals with it rather nicely although very briefly).

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n25

about this see Plot. 1, 3, 4-5. Dialectics is the ability to say about anything in logos what it is and in how differs from others and what is unity of them. Also the knowledge of beings and the process of their being, how many there are of them, and the same - about non-beings. Methods of episteme, diairesis, synthesis. Reality, methodical development, and simultaneous containment of theorems and things in it.

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n26

therefore, dialectics, originating from the ancient myth, ends in myth also, but not in the plain but logically constructed myth. See Plot. 3, 2, 13 (Adrasteia); 5, 8, 2, 13; 6, 9, 9 (Aphrodite); 5, 5, 6 (Apollo); 4, 3, 12 (Dionysos); 4, 4, 27 (Demetra); 5, 5, 7 (Athena); 5, 1, 4, 7; 5, 8, 13 (Kronos); 4, 3, 14 (Prometheus).

Procl. in Plat. theol.:

1. Divine world: the One (to hen) - unspoken.
2. Noetic world:
2.1. noys: